X(96) Isogonal conjugate of X(52)

isogonal conjugate of X(52)

Triangle center X(52) is the orthocenter of orthic triangle.
The orthic triangle A'B'C' is the triangle formed by the feed of the altitudes of the triangle ABC.
A'', B'', and C'' are the feet of the altidudes of this orthic triange.
The altitudes A'A'', B'B'', and C'C'' cross at the triangle center X(52).
The isogonal conjugate of X52, triangle center X(52) can be constructed as follows:

Reflect the lines AX52, BX52, CX52 about the bisectors of the triangle ABC (=blue lines)

These blue lines cross at the triangle center X(96).
The barycentric coordinates of this point depend on the lenghts of the triangle.